Campbell and Cochrane meet Melino and Yang: Reverse engineering the surplus ratio in a Mehra-Prescott economy

The well-known habit model of Campbell and Cochrane (1999) specifies a process for the 'surplus ratio'-the excess of consumption over habit, relative to consumption-rather than an evolution for the habit stock. This paper shows that Campbell-Cochrane preferences can be accommodated in a Markov chain framework à la Mehra and Prescott (1985) and mapped into an equivalent state-dependent form of the sort studied by Melino and Yang (2003). The equivalence sheds light on the workings of Campbell-Cochrane preferences and the plausibility of upcounting in Melino and Yang's framework. The result may also have some pedagogical value.